It seems that every Lightroom workflow tutorial, article or video always insists on making use of the "Develop" module, which I do not want to use.
For what reason?
LR Develop module has the exact same underlying software as ACR. You will get the exact same results.
But if you are struggling to come up with a workflow, there is a good reason you are struggling. Lightroom was designed as a workflow software, taking you from start to finish of a image management/editing/publishing workflow. If you want to branch out and throw your own unnecessary steps in (using ACR is quite unnecessary), then I believe you will struggle, and there is not a smooth process flow to be found.
As dj suggests, LR is a complete workflow, so it seems you are trying to add extra unnecessary steps. My first thought when I read your post was "why not just use Bridge with Photoshop?"
What is your workflow, now, with Bridge/ACR/Photoshop? What value-added does Lightroom bring to the Bridge/PS/ACR workflow you currently have, and what do you feel LR doesn’t do well that causes you to want to use Bridge/ACR, instead?
The XMP file will save the Develop settings between LR and ACR. ACR will read settings from the XMP files (as long as you have the preference set not to store the settings in a central camera-raw database) whenever you are in Bridge or ACR and ACR will write to the XMP files whenever you click Done to exit, or choose Update XMP or whatever the menu items says.
LR can be told to Synchronize metadata settings, or you can explicitly read and write to the XMP files. LR also reads from the XMP files when you import, and writes to them in the background if you have Automatically write XMP files (or whetaver the phrase is) enabled in Preferences.
If you want to live I both worlds then you need to think about what you’re doing with what XMP files, when, so you don’t overwrite something you work on in the other program. As others have suggested, this is harder than if you just used LR or Bridge/ACR for everything.
Simply right click on your file in Lightroom and choose "Open as Smart Object in photoshop"
Then it will open in photoshop as a layer, Double click to go into Camera RAW, or apply adjustment layer.
When you press save, it will save the layered file back to Lightroom. Any time, choose Open in photoshop for Lightroom and that layered file will be opened in photoshop exactly how you left it off.